Related papers: On the estimation of the convergence rate in the J…
We examine a special case of the multilevel factor model, with covariance given by multilevel low rank (MLR) matrix~\cite{parshakova2023factor}. We develop a novel, fast implementation of the expectation-maximization algorithm, tailored for…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence…
This work extends the factorization method to the inverse scattering problem of reconstructing the shape and location of an absorbing penetrable scatterer embedded in a thin infinite elastic (Kirchhoff--Love) plate. With the assumption that…
This paper presents a finite time convergence analysis for a decentralized stochastic approximation (SA) scheme. The scheme generalizes several algorithms for decentralized machine learning and multi-agent reinforcement learning. Our proof…
We study the Proximal Langevin Algorithm (PLA) for sampling from a probability distribution $\nu = e^{-f}$ on $\mathbb{R}^n$ under isoperimetry. We prove a convergence guarantee for PLA in Kullback-Leibler (KL) divergence when $\nu$…
Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered. A spectral order, parallelizable method for their numerical inversion is…
In this paper, we describe a new algorithm that approximates the extreme eigenvalue/eigenvector pairs of a symmetric matrix. The proposed algorithm can be viewed as an extension of the Jacobi eigenvalue method for symmetric matrices…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
In this paper, we give a spectral approximation result for the Laplacian on submanifolds of Euclidean spaces with singularities by the $\epsilon$-neighborhood graph constructed from random points on the submanifold. Our convergence rate for…
When a matrix has a banded inverse there is a remarkable formula that quickly computes that inverse, using only local information in the original matrix. This local inverse formula holds more generally, for matrices with sparsity patterns…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
We consider the task of sampling with respect to a log concave probability distribution. The potential of the target distribution is assumed to be composite, \textit{i.e.}, written as the sum of a smooth convex term, and a nonsmooth convex…
We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion…
Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the…
The inverse problem of Kohn-Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the…
In this paper we introduce five different algorithms based on method of moments, maximum likelihood and full Bayesian estimation for learning the parameters of the Inverse Gamma distribution. We also provide an expression for the KL…
In previous work, we introduced a method for determining convergence rates for integration methods for the kinetic Langevin equation for $M$-$\nabla$Lipschitz $m$-log-concave densities [arXiv:2302.10684, 2023]. In this article, we exploit…
This work investigates a Bregman and inertial extension of the forward-reflected-backward algorithm [Y. Malitsky and M. Tam, SIAM J. Optim., 30 (2020), pp. 1451--1472] applied to structured nonconvex minimization problems under relative…